Write a MATLAB function pvss that takes as input the coefficient matrix and right hand side of a linear system and returns the parametric vector form of the solution in the following format:

function [sscount, p, V] = pvss(A,b)

sscount = -1 if the system is inconsistent (signaled by a pivot in the last column of rref([A b]).

sscount = 0 if the system has a unique solution (signaled by a lack of free variables)

sscount is the number of free variables of the system (number of columns of V) otherwise

p is the particular solution corresponding to all free variables being equal to zero (empty vector if sscount=-1),

V is the matrix whose columns are homogeneous solutions (i.e. solutins of ) corresponding to one of the free variables equal to 1 while the others are 0 (empty list of columns if sscount <= 0).

The provided template provides code to implement pvss except for the determination of V which can be implemented by completing four four lines in the code marked "UPDATE".

I ALREADY WROTE CODE THAT WORKS FOR THE MOST PART BUT THAT RETURNS THE WRONG VALUE FOR THE VARIABLE SSCOUNT WHEN THE INPUT IS A=[1 2 3; 4 5 6; 7 8 9] and b=[1; 1; 1], BUT IT DOES PRODUCE THE CORRECT OUTPUT WHEN THE INPUT IS A=[1 2 3; 4 5 6; 7 8 9] and b=[2; 1; 1].

below is the code I wrote that needs to be fixed:

function [sscount, p, V] = pvss(A,b)

% For the linear system Ax=b finds the parametric vector form of the solution.

% If no solutions sscount=-1; otherwise, sscount is number of free variables

% p is the particular solution with the free variables equal to zero (empty if sscount== -1)

% ith column of V is the homogeneous solution corresponding to the ith free variable (empty if sscount <= 0)

Augmented = [A b];

[m, n] = size(Augmented);

[R, pclist] = rref(Augmented); % rreduced row echelon form and pivot column list

r = size(pclist,2); % number of pivot columns (rank(A))

% CASE OF AN INCONSISTENT SYSTEM

if r>0 && pclist(r)==n

sscount = -1;

p = zeros(n-1,0);

V = zeros(n-1,0);

return

end

% OBTAIN THE PARTICULAR SOLUTION

p = zeros(n-1,1);

p(pclist) = R(1:r,n);

% OBTAIN THE HOMOGENEOUS SOLUTIONS CORRESPONDING TO EACH FREE VARIABLE (IF ANY)

sscount = n-r; % determine number of free variables (sscount)

if sscount <= 0

V = zeros(n-1, 0);

return

end

fvlist = setdiff(1:n-1, pclist); % find the list of free variables

V = zeros(n-1, sscount-1); % initialize V

V(pclist,1:r) = eye(r); % copy appropriately pivot rows of V from identity matrix

V(fvlist,:) = -R(r+1:m, pclist) * V(pclist,:); % set free rows of V appropriately

%sscount = sscount - 1;

end